Soon after Miss Stacey arrives, there's a scene where she's helping Diana with a mathematics problem. There's a right angled triangle and she is using Pythagoras to calculate the length of the hypotenuse. In the scene she calculates the hypotenuse to by 1700 but the correct answer would be 1886 (approximately).
Anne recites a poem (the Highwayman by Alfred Noyes) that was published in 1905, years after that scene in Anne of Green Gables (book or movie) took place.